Convert 7.0055 into a mixed number in simplest form

Vera is using her phone. It’s battery life is down to 2/5 and it drains another 1/9 every hour. How many hours will her battery

Otrada [13]

her battery will lost for 3.6 hours

8 0

3 years ago

A safety officer wants to prove that μ = the average speed of cars driven by a school is less than 25 mph. Suppose that a random

melomori [17]

Answer:

$t=\frac{24-25}{\frac{2.2}{\sqrt{14}}}=-1.70$

$p_v =P(t_{(13)}$

If we compare the p value and the significance level given $\alpha=0.05$ and we can see that $p_v>\alpha$ so we can conclude that we have enough evidence to FAIL reject the null hypothesis, so we can't conclude that the true average speed is lower than 25 mph at 5% of signficance.

Step-by-step explanation:

Data given and notation

$\bar X=24$ represent the sample mean

$s=2.2$ represent the sample standard deviation

$n=14$ sample size

$\mu_o =25$ represent the value that we want to test

$\alpha=0.05$ represent the significance level for the hypothesis test.

t would represent the statistic (variable of interest)

$p_v$ represent the p value for the test (variable of interest)

State the null and alternative hypotheses.

We need to conduct a hypothesis in order to check if the true mean for the average speed is lower than 25 mph, the system of hypothesis would be:

Null hypothesis: $\mu \geq 25$

Alternative hypothesis: $\mu < 25$

If we analyze the size for the sample is < 30 and we don't know the population deviation so is better apply a t test to compare the actual mean to the reference value, and the statistic is given by:

$t=\frac{\bar X-\mu_o}{\frac{s}{\sqrt{n}}}$ (1)

Calculate the statistic

We can replace in formula (1) the info given like this:

$t=\frac{24-25}{\frac{2.2}{\sqrt{14}}}=-1.70$

P-value

The first step is calculate the degrees of freedom, on this case:

$df=n-1=14-1=13$

Since is a one side test the p value would be:

$p_v =P(t_{(13)}$

Conclusion

If we compare the p value and the significance level given $\alpha=0.05$ and we can see that $p_v>\alpha$ so we can conclude that we have enough evidence to FAIL reject the null hypothesis, so we can't conclude that the true average speed is lower than 25 mph at 5% of signficance.

7 0

3 years ago

Write each sum as a product of the GCF of the two numbers 36 and 45

nika2105 [10]

The GCF of both numbers is 9. So 9 goes outside the parentheses. The numbers multiplied by the GCF to get 36 and 45 are 3 and 5. The answer is 9 ( 3 + 5 )

4 0

3 years ago

Which of the following place value tables shows 40,833?

jolli1 [7]

40,833 has...

4 Ten Thousands

8 Hundreds

3 Tens

3 Ones

6 0

4 years ago

Need help fast please

dalvyx [7]

Answer:

13. The slope for a line that is perpendicular to the line y=4x+8 is -1/4

14. The slope for a line that is perpendicular to the line x=-6 is 0

15. The equation for a line that is perpendicular to the line 8x-4y=12 and passes through the origin is y = - (1/2) x

16. The equation for a line that is perpendicular to the line y=-(1/3)x and passes through the point (0,-10) is y=3x-10

Step-by-step explanation:

13. What is the slope for a line that is perpendicular to the line y=4x+8?

y=mx+b

Comparing with the form slope-intercept, the slope of the given line is the coefficient of x, then the slope of the given line is 4.

A line perpendicular to y=4x+8 must have a slope opposite and inverse, then:

Slope of the perpendicular = - 1/4

14. What is the slope for a line that is perpendicular to the line x=-6?

The line x=-6 is a vertical line. A line perpendicular to the line x=-6 must be a horizontal line (Angle=0°), then:

Slope of the perpendicular = tan Angle = tan 0° = 0

15. Write the equation for a line that is perpendicular to the line 8x-4y=12 and passes through the origin.

8x-4y=12

Isolating y: Subtracting 8x both sides of the equation:

8x-4y-8x=12-8x

-4y=-8x+12

Dividing all the terms by -4:

-4y/(-4)= -8x/(-4)+12/(-4)

y=2x-3

The slope of the given line is 2

The slope of the perpendicular is m=-1/2 (opposite and inverse to the slope of the given line)

The perpendicular passes through the origin:

P1=(0,0)=(x1,y1)→x1=0, y1=0

Using the equation point - slope:

y-y1=m(x-x1)

Replacing the known values:

y-0=(-1/2)(x-0)

y=(-1/2)x

16. Write an equation for a line that is perpendicular to the line y=-(1/3)x and passes through the point (0,-10).

The slope of the given line is -(1/3)

The slope of the perpendicular is m=3/1→m=3 (opposite and inverse to the slope of the given line)

The perpendicular passes through the point:

P1=(0,-10)=(x1,y1)→x1=0, y1=-10

Using the equation point - slope:

y-y1=m(x-x1)

Replacing the known values:

y-(-10)=3(x-0)

y+10=3x

Isolating y: Subtracting 10 both sides of the equation:

y+10-10=3x-10

y=3x-10

8 0

4 years ago